Tens of thousands have protested in Spanish cities in recent days, outraged by the decision of a court in Navarre to clear five men of gang rape, convicting them instead of the lesser offence of sexual abuse. The defence claimed it was consensual, since the woman had not fought back. The court concluded that video shot by the attackers showed the victim surrounded and subjugated to their will, her eyes shut, silent but for cries of pain. Yet they concluded that there was no violence or intimidation, as Spanish law requires for a finding of rape. One judge wanted to acquit the men of everything except stealing her phone.

Prosecutors are appealing against the decision; politicians have rushed to denounce it. Madrid has said it will re-examine sexual offences legislation. In a tweet, Spain’s national police force wrote “No means no” 12 times. As in many places, years of campaigning has helped to change official and public attitudes for the better. How can it be that there is still so far to go?

Though campaigners in Spain have blamed its “patriarchal and macho culture”, the protests chime far and wide. India, too, has just seen demonstrations against sexual violence and the dreadful response of officials and politicians after the rape and murder of two girls, one aged just eight. Last month saw rallies in Belfast and Dublin after the acquittal of two Irish rugby internationals for rape: anger was sparked by the eight-day cross examination of the complainant.

In the US last week, people welcomed Bill Cosby’s conviction for sexual assault, following complaints from multiple women over many years. But while some hailed it as a breakthrough, others warned that it was an anomaly.

The state’s case against any defendant should be tested rigorously. Witnesses must be challenged where necessary and their evidence weighed. Sometimes it will be found wanting. But too often, women who are assaulted suffer a second time.

For some, it happens when the state fails to bring their attackers to court. For others, it happens in trials, through vicious cross-examination designed not to test but undermine their accounts; and through the exploitation of myths about the prevalence of fake accusations and how victims behave. Spanish protesters pointed to cases in which women were murdered for resisting attackers. Cosby’s prosecutors had to bring an expert to testify that “most common knowledge about sexual assault is wrong”.

The primary injustice is to victims. But such cases also discourage other women from reporting assaults. They tell perpetrators they can get away with it. And they send out a broader signal about the acceptable treatment of women.

Protesters around the world (in part galvanised by each other’s courage and solidarity, as with the spread of the #MeToo movement) are sending their own message. Women not only deserve but demand better – and they don’t plan to stop until they get it.